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Theoretical physicist Stephen Hawking is arguably the smartest man in the world right now. His book, A Brief History of Time, has sold millions of copies and made him a veritable icon of scientific knowledge. Despite all that, Hawking's view on the relationship between science and religion is unfortunately mistaken.
In a recent interview with Diane Sawyer, Hawking made some comments that implied science and religion are fundamentally opposed, and that science will win. Here's a brief excerpt from the article:

[E]xploring the origins of time inevitably leads to questions about the ultimate origins of everything and what, if anything, is behind it all.

"What could define God [is thinking of God] as the embodiment of the laws of nature. However, this is not what most people would think of that God," Hawking told Sawyer. "They made a human-like being with whom one can have a personal relationship. When you look at the vast size of the universe and how insignificant an accidental human life is in it, that seems most impossible."

When Sawyer asked if there was a way to reconcile religion and science, Hawking said, "There is a fundamental difference between religion, which is based on authority, [and] science, which is based on observation and reason. Science will win because it works."

The line that separates science from religion is not as clear as Hawking's comments make it seem. Here's why: scientific knowledge depends entirely upon reason. But, as it turns out, reason cannot be explained scientifically. Any attempt to do so only ends up defeating itself.

As Hawking correctly pointed out, science is based on observation and reason. No scientific theory is formed without the employment of human reasoning. Thus, the validity of reason is crucial to the practice of science. Now, if it turned out that we had good reasons to suspect human reasoning is unreliable, then the validity of science would be in question; since the validity of science is dependent on the validity of human reasoning. C.S. Lewis made this same point in his book Miracles, and then took it a step further:

All possible knowledge, then, depends on the validity of reasoning....Unless human reasoning is valid no science can be true. It follows that no account of the universe can be true unless that account leaves it possible for our thinking to be a real insight. A theory which explained everything else in the whole universe but which made it impossible to believe that our thinking was valid, would be utterly out of court. For that theory would itself have been reached by thinking, and if thinking is not valid that theory would, of course, be itself demolished.[1]

Lewis' point is this: for any scientific theory, if that theory calls into question the validity of human reasoning, then the theory fails; because that same theory will involve the use of reason. And if we can't trust reason, then we can't trust the theory. Thus, the theory will have defeated itself.

It is clear from the interview that Hawking believes science has shown God's existence is "most impossible," because the universe is so big, and human life so apparently insignificant. In other words, for Hawking, a scientific view of the world will be atheistic. However, if science really entails the belief that God's existence is "most impossible," as Hawking says, then we have reason to doubt the validity of human reasoning, and therefore reason to doubt Hawking's claim.

If there is no God, then our reasoning abilities are the result of some material process of nature - such as Darwinian evolution. In other words, if God does not exist, then our rational faculties were most certainly built through irrational means. This is a problem for the following reason: whenever we suspect that a person's belief is not based on reason, but instead is based on some material or irrational process, we reject his belief as unjustified.

For instance, when people say things like, "You only think this is the best sandwich you've ever had because you're so hungry," or "She believes I am her son because she has Alzheimer's," or "You only believe in God because it makes you feel safe," they are rejecting a particular belief because they suspect it is based on material/irrational processes - hunger, brain deterioration, a feeling of safety. In other words, most people would agree that if a belief is based on something irrational, then the belief is unjustified. If Hawking's view of the universe is correct however, then this is not only true of the particular beliefs just mentioned, it is true of all our beliefs, including Hawking's!

If there is no God, and Darwinian evolution is true, then human reason came about through a blind irrational process of nature that simply preserves things that give organisms a better chance of surviving and reproducing. If that is the case, then human reason is invalid. Think about it. If you asked someone why they believe the earth is round, and they answered, "because it will help me to stay alive and produce more offspring than my competitors" you would say their belief was unjustified. If Hawking's view of the universe is correct, then any belief we may hold - our rational process in its entirety - is ultimately based on its ability to help us survive and produce more offspring. This calls into question the validity of all human reasoning. But, as we established earlier, scientific theories depend on reasoning. If we can't trust human reasoning, then we can't believe any scientific theory. Thus, if Hawking's view is correct, then we should doubt it. His view defeats itself.[2]

If science cannot adequately explain human reason - lest it undercut its own validity - then what is left as an explanation? It will be some view that leaves open the possibility of the supernatural - some view that doesn't see God's existence as "most impossible." Religion then becomes a valid option. Science and religion are not fundamentally opposed. In fact, they need each other.